Question

There are 3 equal point charges qq at the vertices of an equilateral triangle of side length aa. What is the work that you must do to bring a point charge 4q4q from infinity to the center of the triangle?

Answer 1

center of triangle is centroid of triangle.

so, radius of centre of equilateral triangle = 2/3 × median of triangle

= 2/3 × √3a/2

= a/√3

[ as we know, for equilateral triangle, medium is same as altitude. so, length of altitude = √(a² - a²/4) = √3a/2 = length of median ]

now, workdone by charge particle 4q , W = 4q × potential at centre of triangle

= 4q × [ kq/(a/√3) + kq/(a/√3) + kq/(a/√3)]

= 4q × 3√3kq/a

= 12√3kq²/a

hence, answer is 12√3kq²/a